In British and international law as many of us now, the power of a signature can indeed not just be considered contractually binding, but also legally so too. As you are purchasing a ticket from the TOC, you are effectively entering into a contract with the company until the completion of the journey.
The legal basis of travel on the railway is contractual. As well as the contract, there are also various statutory rights and responsibilities for users of the railway.
There is no 'effectively entering into a contract' - when you ask to purchase a ticket and the ticketing provider sells you that ticket you are entering into a contract subject to the terms and conditions found in the
National Rail Conditions of Travel as well as terms implied into that contract by consumer law.
These mainly includes things such as when you are entitled to travel, and with how many people etc, but by using the senior railcard you mention, you are also effectively entering into a contract saying you will use it only when valid, for example you won't continue to use it if you no longer are eligible etc.
By not signing the railcard, you are effectively saying the card is not contractually binding for you nor the company, so therefore the TOC does not have to abide by the discount it entitles you too. In short this means you could be charged again for the journey you made whilst applying the railcard discount, but I view this as extremely unlikely!
As my contract law tutor at university would have said, "when did the contract crystallise?". A contract needs offer, acceptance, consideration and intention to create legal relations; when all four are in place the contract crystallises and comes into effect. When a customer asks to buy a railcard (offer) and offers to pay the fee in return for the railcard (consideration), intending to be bound by the terms of the railcard (intention to create legal relations), then the Railcard provider agrees to sell the railcard for that fee (agreement) then the contract crystallises at that time - not at a later time when the railcard is signed.
Paragraph 2.1 of the
Senior Railcard Terms & Conditions says that a physical Senior Railcard is invalid until signed, and paragraph 2.8.1 says that a physical Senior Railcard must be signed when shown to a member of staff along with a railcard discounted ticket. Failure to show a signed railcard can result in you being charged full fare and, when relevant, a Penalty Fare (paragraph 2.9).
It is open to debate whether sufficient prominence is given to these terms for them to be incorporated into the contract and therefore binding on the Railcard holder (as required by
Thornton v Shoe Lane Parking Ltd [1970] EWCA Civ 2, [1971] 2 QB 163) and whether these terms are open to attack for unfairness using
section 62 of the Consumer Rights Act 2015. Such attacks based on contract law might be inadequate because they cannot change the obligations on the passenger and remedies available to the rail company under the byelaws and criminal law, the existence of which could leave a Railcard holder needing to mount a challenge to the validity of these terms in the civil courts in order to have a defence in a prosecution in the criminal courts. Rather than getting yourself embroiled in all this complexity, the simplest answer is "just sign your Railcard and don't take a chance".
A member of staff being handed an unsigned Railcard may well hand it back and ask the holder to sign it - but they could treat the matter as ticketless travel and it might take a lengthy legal battle to try to overturn the terms invalidating an unsigned Railcard.